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A Fast Derivative-Free Iteration Scheme for Nonlinear Systems and Integral Equations

Author

Listed:
  • Mozafar Rostami

    (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 15743-65181, Iran)

  • Taher Lotfi

    (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 15743-65181, Iran)

  • Ali Brahmand

    (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 15743-65181, Iran)

Abstract

Derivative-free schemes are a class of competitive methods since they are one remedy in cases at which the computation of the Jacobian or higher order derivatives of multi-dimensional functions is difficult. This article studies a variant of Steffensen’s method with memory for tackling a nonlinear system of equations, to not only be independent of the Jacobian calculation but also to improve the computational efficiency. The analytical parts of the work are supported by several tests, including an application in mixed integral equations.

Suggested Citation

  • Mozafar Rostami & Taher Lotfi & Ali Brahmand, 2019. "A Fast Derivative-Free Iteration Scheme for Nonlinear Systems and Integral Equations," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:637-:d:249477
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    References listed on IDEAS

    as
    1. F. Soleymani & M. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "A Class of Steffensen-Type Iterative Methods for Nonlinear Systems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, April.
    2. Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
    3. Ahmad, F. & Soleymani, F. & Khaksar Haghani, F. & Serra-Capizzano, S., 2017. "Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 199-211.
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